1. In a 5- to 6-quart pan over high heat, break meat into chunks with a spoon. Add onion and garlic and stir often until onion is limp, about 5 minutes.
2. Add broth, tomato sauce, wine, oregano, pasta, and 2 cups water. Stirring often, bring to a boil and cook until pasta is just tender to bite, about 10 minutes.
3. Rinse, drain, and coarsely chop arugula. Add arugula and beans to pasta mixture. Stir occasionally until soup is boiling, about 3 minutes.
4. Ladle into bowls and add cheese and pepper to taste.